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Operations-Research-Spektrum

, Volume 17, Issue 2–3, pp 87–92 | Cite as

A generalized permutation approach to job shop scheduling with genetic algorithms

  • Christian Bierwirth
Article

Abstract

In order to sequence the tasks of a job shop problem (JSP) on a number of machines related to the technological machine order of jobs, a new representation technique — mathematically known as “permutation with repetition” is presented. The main advantage of this single chromosome representation is — in analogy to the permutation scheme of the traveling salesman problem (TSP) — that it cannot produce illegal operation sequences. As a consequence of the representation scheme a new crossover operator preserving the initial scheme structure of permutations with repetition will be sketched. Its behavior is similar to the well known Order-Crossover for simple permutation schemes. Actually theGOX operator for permutations with repetition arises from aGeneralisation ofOX. Computational experiments show, that GOX passes the information from a couple of parent solutions efficiently to offspring solutions. Together, the new representation and GOX support the cooperative aspect of genetic search for scheduling problems strongly.

Key words

Genetic algorithms job shop scheduling permutation operators 

Zusammenfassung

Im vorliegenden Beitrag wird ein neuer Ansatz zur genetischen Repräsentation des Maschinenbelegungsproblems vorgestellt. Der Ansatz basiert auf dem bekannten Konzept der Repräsentation von Rundreiseproblemen durch Permutationen. In Erweiterung dieses Konzepts werden „Permutationen mit Wiederholung“ zur Kodierung von Lösungen eingesetzt. Die zentrale Schwierigkeit vorangegangener Ansätze, nämlich die Behandlung unzulässiger Genotypen, entfällt vollständig. Permutationen mit Wiederholung repräsentieren grundsätzlich zulässige Lösungen des betrachteten Problems. Aus einer Generalisierung der permutationsbewahrenden Order-Crossover Technik (OX) wird der KreuzungsoperatorGOX (GeneralisiertesOX) für Permutationen mit Wiederholung abgeleitet. In einer Testreihe wird die mit dem neuen Konzept zu erreichende Lösungsgüte untersucht. Es zeigt sich, daß die kooperative Komponente der genetischen Suche durch die Repräsentation und ihren Kreuzungsoperator verstärkt wird. Ein einfacher genetischer Algorithmus erzielt Lösungsgüten, die zuvor nur von stark hybriden Algorithmen erreicht wurden.

Schlüsselwörter

Genetische Algorithmen Maschinenbelegungsplanung permutationsbewahrende Operatoren 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Christian Bierwirth
    • 1
  1. 1.Department of EconomicsUniversity of BremenBremenGermany

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